| Outline of Final Research Achievements |
The main subject of my research is nonlinear Partial Differential Equations, and in particular I have made some special effort to the study on the Hamilton-Jacobi (HJ) equation. This equation is an important fundamental equation for various branches of science like classical mechanics, geometric optics, calculus of variations, optimal control and differential games. During the project period, I focused on problems related to various properties of viscosity solutions of Hamilton-Jacobi equations appearing in the context of classical mechanics and crystal growth. In particular, I have worked on the following topics: (a) Asymptotic analysis on Hamilton-Jacobi-Bellman equations (the large time behavior, homogenization), (b) Analysis on the birth-and-spread model equation appearing in the crystal growth, (c) Selection problems for the mean field game. I got several new and important results and published 9 (peer-reviewed) papers.
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